Abstract
In this paper, we discuss the idea of complex phase synchronization in complex nonlinear structures with chaotic conduct. The CPHS combines two types of common synchronizations, which are phase synchronization and anti phase synchronization. A general scheme has been proposed to study the CPHS. Through this scheme, complex control functions are assigned to obtain effective CPHS. For example, we study the CPHS in regards pair chaotic complex Lü structures including incompletely evolving for nonlinear terms. Numerical figures are drawn to prove our plan’s validity. The consequences of the CPHS are exploited in secure communications. The error function resulting from the definition of the CPHS was used as a key to retrieve the encrypted message.